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MARCO MACKAAIJ. PhD in Mathematics, Instituto Superior Técnico, Lisbon, Portugal, 1999/12/21. Associate Professor in Mathematics at the Universidade do Algarve. Research: categorified quantum algebras, 2-representation theory and link homology.
Identification

Personal identification

Full name
MARCO MACKAAIJ

Citation names

  • MACKAAIJ, MARCO
  • Marco Mackaay

Author identifiers

Ciência ID
F810-F5CB-9F35
ORCID iD
0000-0001-9807-6991

Knowledge fields

  • Exact Sciences - Mathematics - Pure Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
Dutch Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2)
English Advanced (C1) Advanced (C1) Advanced (C1) Advanced (C1)
Portuguese Advanced (C1) Advanced (C1) Advanced (C1) Advanced (C1)
Education
Degree Classification
1999/12/21
Concluded
 Doutoramento em Matemática (Doutoramento)
Universidade de Lisboa Instituto Superior Técnico, Portugal
"Spherical 2-categories and 4-manifold invariants" (THESIS/DISSERTATION)
 Aprovado
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
2023/05/02 - Current Associate Professor (University Teacher) Universidade do Algarve, Portugal
Universidade do Algarve Faculdade de Ciências e Tecnologia, Portugal
2000/01/27 - 2023/05/01 Assistant Professor (University Teacher) Universidade do Algarve, Portugal
Universidade do Algarve Faculdade de Ciências e Tecnologia, Portugal
1998/11/30 - 2000/01/26 Assistant (University Teacher) Universidade do Algarve, Portugal

Others

Category
Host institution 		Employer
2000/09/01 - 2002/08/31 Postdoctoral researcher University of Nottingham, United Kingdom
1996/07/16 - 1998/11/29 Junior teaching assistant Universidade do Algarve, Portugal
Projects

Grant

Designation Funders
2018/07 - 2021/06 Higher Structures and Applications
PTDC/MAT-PUR/31089/2017
 Fundação para a Ciência e a Tecnologia, I.P.
2013/05 - 2016/04 Geometry and Mathematical-Physics
Provided by PTCRIS: 126662
 Fundação para a Ciência e a Tecnologia, I.P.
2010/01 - 2013/06 New Geometry and Topology
Provided by PTCRIS: 101503
 Fundação para a Ciência e a Tecnologia, I.P.
2007/01 - 2009/12 Quantum Topology
Provided by PTCRIS: 82619
 Fundação para a Ciência e a Tecnologia, I.P.
2005/06 - 2008/06 Quantum Topology
Provided by PTCRIS: 60352
 Fundação para a Ciência e a Tecnologia, I.P.
2007/03 - 2008/02 Symmetries, gravity and strings
Provided by PTCRIS: 63916
 Fundação para a Ciência e a Tecnologia, I.P.
Outputs

Publications

Journal article
  1. Marco Mackaay; Vanessa Miemietz; Pedro Vaz. "Evaluation birepresentations of affine type A Soergel bimodules". Advances in Mathematics (2024): http://dx.doi.org/10.1016/j.aim.2023.109401.
    10.1016/j.aim.2023.109401
  2. Mackaay, M.; Mazorchuk, V.; Miemietz, V.; Tubbenhauer, D.; Zhang, X.. "Simple transitive 2-representations of Soergel bimodules for finite Coxeter types". Proceedings of the London Mathematical Society (2023): http://www.scopus.com/inward/record.url?eid=2-s2.0-85147705579&partnerID=MN8TOARS.
    10.1112/plms.12515
  3. "Finitary birepresentations of finitary bicategories". Forum Mathematicum 33 5 (2021): 1261-1320. http://dx.doi.org/10.1515/forum-2021-0021.
    10.1515/forum-2021-0021
  4. MacKaay, M.; Mazorchuk, V.; Miemietz, V.; Tubbenhauer, D.. "Trihedral soergel bimodules". Fundamenta Mathematicae 248 3 (2020): 219-300. http://www.scopus.com/inward/record.url?eid=2-s2.0-85083429841&partnerID=MN8TOARS.
    10.4064/fm566-3-2019
  5. MACKAAIJ, MARCO; Tubbenhauer, D.. "Two-color Soergel Calculus and Simple Transitive 2-representations". Canadian Journal of Mathematics 71 6 (2019): 1523-1566. http://dx.doi.org/10.4153/cjm-2017-061-2.
    10.4153/cjm-2017-061-2
  6. Kildetoft, T.; Mackaay, M.; Mazorchuk, V.; Zimmermann, J.. "Simple transitive 2-representations of small quotients of soergel bimodules". Transactions of the American Mathematical Society 371 8 (2019): 5551-5590. http://www.scopus.com/inward/record.url?eid=2-s2.0-85059800140&partnerID=MN8TOARS.
    10.1090/tran/7456
  7. Mackaay, M.; Yonezawa, Y.. "slN-web categories and categorified skew Howe duality". Journal of Pure and Applied Algebra 223 5 (2019): 2173-2229. http://www.scopus.com/inward/record.url?eid=2-s2.0-85050394795&partnerID=MN8TOARS.
    10.1016/j.jpaa.2018.07.013
  8. Mackaay, M.; Mazorchuk, V.; Miemietz, V.; Tubbenhauer, D.. "Simple transitive 2-representations via (co-)algebra 1-morphisms". Indiana University Mathematics Journal 68 1 (2019): 1-33. http://www.scopus.com/inward/record.url?eid=2-s2.0-85064335131&partnerID=MN8TOARS.
    Published • 10.1512/iumj.2019.68.7554
  9. Marco Mackaay; Volodymyr Mazorchuk; Vanessa Miemietz; Xiaoting Zhang. "ANALOGUES OF CENTRALIZER SUBALGEBRAS FOR FIAT -CATEGORIES AND THEIR -REPRESENTATIONS". Journal of the Institute of Mathematics of Jussieu (2018): https://doi.org/10.1017/S1474748018000555.
    10.1017/S1474748018000555
  10. Marco Mackaay; Alistair Savage. "Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification". Journal of Algebra 505 (2018): 150-193. https://doi.org/10.1016/j.jalgebra.2018.03.004.
    10.1016/j.jalgebra.2018.03.004
  11. Mackaay, M.; Webster, B.. "Categorified skew Howe duality and comparison of knot homologies". Advances in Mathematics 330 (2018): 876-945. http://www.scopus.com/inward/record.url?eid=2-s2.0-85054039028&partnerID=MN8TOARS.
    10.1016/j.aim.2018.03.034
  12. Mackaay, M.; Mazorchuk, V.. "Simple transitive 2-representations for some 2-subcategories of Soergel bimodules". Journal of Pure and Applied Algebra 221 3 (2017): 565-587. http://www.scopus.com/inward/record.url?eid=2-s2.0-84979713650&partnerID=MN8TOARS.
    10.1016/j.jpaa.2016.07.006
  13. Mackaay, M.; Thiel, A.-L.. "Categorifications of the extended affine Hecke algebra and the affine q-Schur algebra S(n, r) for 3 = r < n". Quantum Topology 8 1 (2017): 113-203. http://www.scopus.com/inward/record.url?eid=2-s2.0-85016118190&partnerID=MN8TOARS.
    10.4171/QT/88
  14. MACKAAIJ, MARCO. "A diagrammatic categorification of the affine q-schur algebra s (n; n) for n = 3". Pacific Journal of Mathematics 278 (1) ,pp.201-233 (2015): http://msp.org/pjm/2015/278-1/p08.xhtml.
    10.2140/pjm.2015.278.201
  15. MACKAAIJ, MARCO. "A diagrammatic categorification of the q-schur algebra". Quantum Topology Volume 4, Issue 1, 2015, Pages 1-75 (2015): https://www.ems-ph.org/journals/show_abstract.php?issn=1663-487X&vol=4&iss=1&rank=1.
    10.4171/QT/34
  16. Mackaay, M.; Pan, W.; Tubbenhauer, D.. "The Sl3-web algebra". Mathematische Zeitschrift 277 1-2 (2014): 401-479. http://www.scopus.com/inward/record.url?eid=2-s2.0-84901262913&partnerID=MN8TOARS.
    10.1007/s00209-013-1262-6
  17. Mackaay, M.. "The slN-web algebras and dual canonical bases". Journal of Algebra 409 (2014): 54-100. http://www.scopus.com/inward/record.url?eid=2-s2.0-84898797516&partnerID=MN8TOARS.
    10.1016/j.jalgebra.2014.02.036
  18. MACKAAIJ, MARCO. "Erratum: A remark on Rasmussen’s invariant of knots". J. Knot and its Ramifications 22(1) (2013), 1392001, 1 p (2013):
    10.1142/S0218216513920016
  19. Khovanov, M.; Lauda, A.D.; Mackaay, M.; Stosíc, M.. "Extended graphical calculus for categorified quantum sl(2)". Memoirs of the American Mathematical Society 219 1029 (2012): 1-87. http://www.scopus.com/inward/record.url?eid=2-s2.0-84863665494&partnerID=MN8TOARS.
    10.1090/S0065-9266-2012-00665-4
  20. Mackaay, M.; Stošic, M.; Vaz, P.. "The 1,2-coloured homfly-pt link homology". Transactions of the American Mathematical Society 363 4 (2011): 2091-2124. http://www.scopus.com/inward/record.url?eid=2-s2.0-79951831799&partnerID=MN8TOARS.
    10.1090/S0002-9947-2010-05155-4
  21. MACKAAIJ, MARCO. "The diagrammatic Soergel category and sl(N)-foams". Int. J. Math. and Math. Sci., vol. 2010, Article ID 468968, 2010 (2010): http://www.hindawi.com/journals/ijmms/2010/468968/abs/.
    10.1155/2010/468968
  22. Mackaay, M.; Stošic, M.; Vaz, P.. "Sl(N)-link homology (N= 4) using foams and the Kapustin-Li formula". Geometry and Topology 13 2 (2009): 1075-1128. http://www.scopus.com/inward/record.url?eid=2-s2.0-74249100145&partnerID=MN8TOARS.
    10.2140/gt.2009.13.1075
  23. Mackaay, M.; Vaz, P.. "The foam and the matrix factorization sl3 link homologies are equivalent". Algebraic and Geometric Topology 8 1 (2008): 309-342. http://www.scopus.com/inward/record.url?eid=2-s2.0-72949110612&partnerID=MN8TOARS.
    10.2140/agt.2008.8.309
  24. Mackaay, M.; Vaz, P.. "The universal sl3-link homology". Algebraic and Geometric Topology 7 1 (2007): 1135-1169. http://www.scopus.com/inward/record.url?eid=2-s2.0-62549096499&partnerID=MN8TOARS.
    10.2140/agt.2007.7.1135
  25. Mackaay, M.; Turner, P.; Vaz, P.. "A remark on Rasmussen's invariant of knots". Journal of Knot Theory and its Ramifications 16 3 (2007): 333-344. http://www.scopus.com/inward/record.url?eid=2-s2.0-34247882696&partnerID=MN8TOARS.
    10.1142/S0218216507005312
  26. Mackaay, M.; Turner, P.. "Bar-Natan's Khovanov homology for coloured links". Pacific Journal of Mathematics 229 2 (2007): 429-446. http://www.scopus.com/inward/record.url?eid=2-s2.0-57449107551&partnerID=MN8TOARS.
    10.2140/pjm.2007.229.429
  27. Barrett, J.W.; Mackaay, M.. "Categorical representations of categorical groups". Theory and Applications of Categories 16 10 (2006): 529-557. http://www.scopus.com/inward/record.url?eid=2-s2.0-33748333184&partnerID=MN8TOARS.
  28. MACKAAIJ, MARCO. "A note on the holonomy in twisted bundles". Cah. Topol. G´eom. Diff´er. Cat´eg. 44 (2003), no. 1, 39-62. (2003): https://eudml.org/doc/91665.
  29. Mackaay, M.; Picken, R.. "Holonomy and parallel transport for Abelian gerbes". Advances in Mathematics 170 2 (2002): 287-339. http://www.scopus.com/inward/record.url?eid=2-s2.0-0037174517&partnerID=MN8TOARS.
    10.1016/S0001-8708(02)92085-2
  30. Mackaay, M.. "Finite groups, spherical 2-categories, and 4-manifold invariants". Advances in Mathematics 153 2 (2000): 353-390. http://www.scopus.com/inward/record.url?eid=2-s2.0-0034632264&partnerID=MN8TOARS.
    10.1006/aima.1999.1909
  31. Mackaay, M.. "Spherical 2-categories and 4-manifold invariants". Advances in Mathematics 143 2 (1999): 288-348. http://www.scopus.com/inward/record.url?eid=2-s2.0-0033541882&partnerID=MN8TOARS.
    10.1006/aima.1998.1798
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2023/01/25 2-Representations of affine type A Soergel bimodules: some examples and observations. TQFT-club seminar
Instituto Superior Técnico (Lisboa)
2022/07/20 2-Representations of affine type A Soergel bimodules: some examples and observations. Algebra and Geometry Seminar
Universidade do Porto (Porto)
2022/05/03 2-Representations of affine type A Soergel bimodules: some examples and observations. Uppsala Algebra Seminar
University of Uppsala (Uppsala, Sweden)
2022/03/14 2-Representations of affine type A Soergel bimodules: some examples and observations. Pure Mathematics Seminar
University of East Anglia (Norwich, United Kingdom)
2019/07/12 The 2-representation theory of Soergel bimodules of finite Coxeter type Representations of monoidal categories and 2-categories
University of East Anglia (Norwich, United Kingdom)
2019/07/11 Finitary 2-representations and (co)algebra 1-morphisms Representations of monoidal categories and 2-categories
University of East Anglia (Norwich, United Kingdom)
2019/06/17 The 2-representation theory of Soergel bimodules. Mathematical Physics Seminar
University of Zurich (Zurique, Switzerland)
2019/04/23 The 2-representation theory of Soergel bimodules. Algebra and Geometry Seminar
Uppsala University (Uppsala, Sweden)
2019/01/24 The 2-theory of Soergel bimodules of finite Coxeter type: a road map to the complete classification of all simple transitive 2-representations. Geometry and Topology Seminar
Universidade do Porto (Porto, Portugal)
2019/01/23 The 2-representation theory of Soergel bimodules Seminário de Álgebra
Universidade de Coimbra (Coimbra, Portugal)
2019/01/10 The 2-theory of Soergel bimodules of finite Coxeter type: a road map to the complete classification of all simple transitive 2-representations. Topological Quantum Field Theory Seminar
Instituto Superior Técnico (Lisboa, Portugal)

Jury of academic degree

Topic
Role 		Candidate name (Type of degree)
Institution / Organization
2023/06/23 On Rasmussen's s-invariant and the search for exotic definite 4-manifolds.
(Thesis) Arguer
 João Miguel Rebelo de Oliveira (Master)
Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
2022/07/20 Hecke Algebras and Topological Quantum Field Theories
(Thesis) Main arguer
 Bernardo Mariz Ferreira Leite da Cunha (Master)
Universidade do Porto, Portugal
2019/07/17 Representations on diagrams of categories and applications to parabolic bundles
(Thesis) Main arguer
 Rui Rodrigues de Abreu Fernandes Prezado (Master)
Universidade do Porto, Portugal
2017/10/28 Pseudomonads and Descent
(Thesis) Arguer
 Fernando Lucatelli Nunes (PhD)
Universidade de Coimbra, Portugal
2016/09/30 The quotient module, coring depth and factorisation algebra
(Thesis) Main arguer
 Alberto Hernandez Alvarez (PhD)
Universidade do Porto, Portugal
2016/01/19 Simple transitive 2-representations of Soergel bimodules in type B2 (tese de "Licentiate")
(Thesis) Main arguer
 Jacob Zimmermann (Other)
Uppsala Universitet, Sweden
2014/09/19 The Depth Theory of a Hopf algebra in its Smash Product
(Thesis) Main arguer
 Christopher J. Young (PhD)
Universidade do Porto, Portugal
2013/07/10 Sur l'homologies sl(3) des enchevêtrements; algèbres de Khovanov-Kuperberg
(Thesis) Main arguer
 Louis-Hadrien Robert (PhD)
Université Paris Diderot, France
2013/07/02 Categorification and applications in topology and representation theory
Thesis Member
 Daniel Tubbenhauer (PhD)
Georg-August-Universität Göttingen, Germany
2013/03/22 Mapping spaces of Gray-categories
(Thesis) Main arguer
 Björn Gohla (PhD)
Universidade do Porto, Portugal
2010/07/29 Odd Khovanov homology for virtual knots
Thesis Member
 Diana Manuel Fernandes Tavares (Master)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2009/12/23 Geometric quantization and degenerations of complex structures for two families of compact manifolds
Thesis Member
 Thomas Baier (PhD)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2008/07/08 A categorification of the quantum sl(N)-link polynomials using foams
Supervisor
 Pedro Vaz (PhD)
Universidade do Algarve - Campus de Gambelas, Portugal
2006/03/31 Khovanov homology of links and graphs
(Thesis) Arguer
 Marko Stosic (PhD)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2003/11/28 Homotopy Quantum Field Theories
(Thesis) Arguer
 Gonçalo Violante Rodrigues (PhD)
Universidade de Lisboa Instituto Superior Técnico, Portugal

Course / Discipline taught

Academic session Degree Subject (Type) Institution / Organization
2022/07/11 - 2022/07/15 Categorification Research School on Bicategories, Categorification and Quantum Theory (Doctor of Philosophy) London Mathematical Society, United Kingdom

University of Leeds, United Kingdom